belief networks

Spectral detection on sparse hypergraphs

We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where the number …

Replica analysis and approximate message passing decoder for superposition codes

Superposition codes are efficient for the additive white gaussian noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian approximate message passing decoder based on a …